Subgroups — Dic₄₀₀ #13097656

Order 1600.

45 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₂₀₀	C₂	1	2	yes	maximal
2	C₂₅×C₃₂	C₂	1	1	yes	maximal, characteristic
3	Dic₁₀₀	—	2	2	no	—
4	C₁₆×C₂₅	C₂²	1	1	yes	characteristic
5	Dic₈₀	—	5	1	no	maximal
6	Dic₅₀	—	4	2	no	—
7	C₈×C₂₅	D₄	1	1	yes	characteristic
8	Dic₄₀	—	5	2	no	—
9	C₅×C₃₂	D₅	1	1	yes	characteristic
10	C₄×C₂₅	D₈	1	1	yes	characteristic
11	Dic₂₅	—	8	2	no	—
12	Dic₂₀	—	10	2	no	—
13	C₅×C₁₆	C₂×D₅	1	1	yes	characteristic
14	Q₆₄	—	25	1	no	Sylow
15	C₂×C₂₅	D₁₆	1	1	yes	characteristic
16	Dic₁₀	—	20	2	no	—
17	C₅×C₈	D₂₀	1	1	yes	characteristic
18	Q₃₂	—	25	2	no	—
19	C₃₂	D₂₅	1	1	yes	characteristic
20	C₂₅	Q₆₄	1	1	yes	characteristic, complemented, Sylow
21	C₄×C₅	D₄₀	1	1	yes	characteristic
22	Dic₅	—	40	2	no	—
23	Q₁₆	—	50	2	no	—
24	C₁₆	C₂×D₂₅	1	1	yes	characteristic
25	C₂×C₅	D₈₀	1	1	yes	characteristic
26	Q₈	—	100	2	no	—
27	C₈	D₁₀₀	1	1	yes	characteristic
28	C₅	Dic₈₀	1	1	yes	characteristic
29	C₄	—	200	2	no	—
30	C₄	D₂₀₀	1	1	yes	characteristic
31	C₂	D₄₀₀	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
20. C₂₅	Q₆₄	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.